Question

a moving ball of mass 0.1 kg undergoes an Elastic head on collision with another ball at rest after frozen the first body was at one third of its origin speed while the second wall stars moving forward find the mass of the second wall .​

Answer 1

Mass of moving ball, $\sf{m_1=0.1\ kg}$

Let mass of second ball be $\sf{m_2.}$

Initial velocity of second ball, $\sf{u_2=0}$

Final velocity of first ball is one - third of its initial velocity but in opposite direction, i.e., $\sf{v_1=-\dfrac{u_1}{3}.}$

Since the collision is elastic, the final velocity of first ball is given by,

$\sf{\longrightarrow v_1=\left(\dfrac{m_1-m_2}{m_1+m_2}\right)u_1+\left(\dfrac{2m_1m_2}{m_1+m_2}\right)u_2}$

$\sf{\longrightarrow -\dfrac{u_1}{3}=\left(\dfrac{0.1-m_2}{0.1+m_2}\right)u_1+\left(\dfrac{2m_1m_2}{m_1+m_2}\right)(0)}$

$\sf{\longrightarrow -\dfrac{u_1}{3}=\left(\dfrac{0.1-m_2}{0.1+m_2}\right)u_1}$

$\sf{\longrightarrow\dfrac{0.1-m_2}{0.1+m_2}=\dfrac{-1}{3}}$

By rule of componendo and dividendo,

$\sf{\longrightarrow\dfrac{m_2}{0.1}=\dfrac{3-(-1)}{3+(-1)}}$

$\sf{\longrightarrow\dfrac{m_2}{0.1}=2}$

$\sf{\longrightarrow\underline{\underline{m_2=0.2\ kg}}}$

Hence mass of the second ball is 0.2 kg.